25.173 and 25.175, the regulations on static longitudinal stability, repeatedly mention the need to demonstrate a stable relationship of the controls, and impose limits on the free return speed as well. 25.173(d) appears to give a mild alleviation, as it talks of not returning to trim being acceptable provided the achievement of the desired trim speed doesn't require "exceptional attention" from the pilot. But that's about all the alleviation there is.
Operating well on the backside of the power curve would appear to make meeting the requirements a challenge - the 173(d) alleviation probably allows operation at the bottom of the curve but wouldn't help a lot once well on the back side of the curve.
So, barring either a specific alleviation for given type, or a fairly sophisticated control scheme, the regs seem to written to force operation no further back than the bottom of the curve.